https://file.aiquickdraw.com/mathbot/file/1728108698711fh45rfcr.jpg

The problem asks to find \((g \circ f)(-4)\), which represents the composition of two functions, \(g(x)\) and \(f(x)\).

From the image, we see that:
- \(g(x) = x + 2\)
- \(h(x) = x^3 - 2x\)

But it's unclear whether you're meant to compose \(g\) with \(f(x)\) or \(h(x)\). I will assume that \(f(x) = h(x)\), and thus \(f(x) = x^3 - 2x\). If this assumption is incorrect, feel free to clarify!

Now, let's proceed step by step:

1. The composition of functions means evaluating \(g(f(x))\). That is, we first evaluate \(f(x)\), and then substitute the result into \(g(x)\).
2. We need to find \((g \circ f)(-4)\), which means evaluating \(f(-4)\) and then using that value in \(g(x)\).

Let's calculate that:

- First, evaluate \(f(-4)\):

\[
f(x) = x^3 - 2x
f(-4) = (-4)^3 - 2(-4) = -64 + 8 = -56
\]

- Now, use this result in \(g(x)\):

\[
g(x) = x + 2
g(-56) = -56 + 2 = -54
\]

Therefore, \((g \circ f)(-4) = -54\).

Do you have any questions or would you like a deeper explanation?

Here are some related questions you might find helpful:
1. What are function compositions and how do they work in general?
2. What if \(h(x)\) was not the same as \(f(x)\)?
3. Can we generalize the process for any two functions \(g(x)\) and \(f(x)\)?
4. What are the practical applications of composing functions?
5. How would this composition change if \(g(x)\) were a more complex function?

**Tip:** When dealing with function compositions, always evaluate the inner function first before substituting into the outer function.

Find (g • f)(-4) where g(x) = x + 2 and h(x) = x^3 - 2x.

Learn how to solve the composition of functions (g ∘ f)(-4) where g(x) = x + 2 and f(x) = x^3 - 2x. This problem involves function composition, polynomial functions, and is suitable for students in Grades 10-12.

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